I occasionally run across people — including law review editors — who seem to take the view that there’s something wrong with starting a sentence with “and,” “but,” or “or.” I don’t see any basis for that view. As Merriam-Webster’s Dictionary of English Usage notes, this doesn’t violate any established usage or grammar practices. It’s commonplace in edited writing, including in legal writing; for instance, a Lexis search for caps(but) and date(> 1/1/2000) in the Supreme Court database found over 900 results since 2000, and a Lexis search for caps(but) and date(> 9/16/2011) in the New York Times database found over 1100 results in just the last week. Nor is this just something new; the Constitution contains sentences that begin with “and” and “but,” as do the works of Dickens and many others.
Moreover, starting a sentence this way is useful: An initial “and,” “but,” or “or” is a good transition that shows the relationship of this sentence to the previous one, with as little formality and complexity as possible. The usual alternatives, such as “however” or “moreover” strike me as stuffier, though sometimes “moreover” adds an emphasis that “and” doesn’t.
Now if you just find these locutions aesthetically displeasing, and want to avoid them in your own writing, there’s not much I can say about that. But I see no basis for faulting others’ use of them, or for editors’ trying to edit them out.